Factor Analysis with female body mass

Load the libraries

knitr::opts_knit$set(root.dir =  rprojroot::find_rstudio_root_file())
knitr::opts_chunk$set(echo = TRUE)
pacman::p_load(tidyverse,vegan,GPArotation,psych,MASS,factoextra,cluster,fpc,FactoMineR,cowplot,broom,modelr,psy)

Create the curated dataset

Log transform what is needed and select the needed columns

source("scripts/theme_geometry.R")
tetrapod_data<- readr::read_csv("data/Tetrapod life history database for maria 31.1.20.csv") %>% 
  drop_na() %>% 
  mutate(log_longevity = log10(Max_Longevity),
         log_clutch = log10(Clutch_Litter_size),
         log_breading_age = log10(Mean_age_at_breeding),
         log_brood = log10(Maximum_Broods_per_year))

## Parsed with column specification:
## cols(
##   Species = col_character(),
##   New_Species = col_character(),
##   Class = col_character(),
##   Order = col_character(),
##   Family = col_character(),
##   Max_Longevity = col_double(),
##   Log_Longevity = col_double(),
##   Clutch_Litter_size = col_double(),
##   Mean_age_at_breeding = col_double(),
##   Maximum_Broods_per_year = col_double(),
##   Log_Hatchling_Mass = col_double(),
##   Origin_Of_Data = col_character(),
##   Log_Female_Mass = col_double()
## )

tetrapod_data<- tetrapod_data %>% 
  dplyr::select(Class, Log_Female_Mass, log_longevity,log_clutch,log_breading_age,log_brood,Log_Hatchling_Mass)

head(tetrapod_data)

## # A tibble: 6 x 7
##   Class Log_Female_Mass log_longevity log_clutch log_breading_age log_brood
##   <chr>           <dbl>         <dbl>      <dbl>            <dbl>     <dbl>
## 1 Amph…         0.544           0.477       2.78          -0.745      0    
## 2 Amph…        -0.0438          0.322       2.80          -0.523      0    
## 3 Amph…         2.05            1.08        2.91          -0.301      0    
## 4 Amph…         0.00303         0.477       1.29          -0.125      0    
## 5 Amph…         1.61            0.322       2.86          -0.0969     0    
## 6 Amph…         0.595           0.614       2.43           0          0.301
## # … with 1 more variable: Log_Hatchling_Mass <dbl>

Running the FA model and extracting the factors for 1,2, and 3 factors. And running the MFA model Storing everything in a nested dataset

#create a nested dataset with all the tetrapods
all_tetra_nest<- tetrapod_data %>% 
  dplyr::select(-Class) %>% 
  nest() %>%
  add_column(Class = "Tetrapods",.before = 1)

#create a nested dataset by class, add the whole tetrapods and map the models into them
tetrapod_nested<- tetrapod_data %>%
  nest(-Class) %>%
  bind_rows(all_tetra_nest) %>% 
  mutate(model.fa1 = map(data, function(df) factanal(df,1,rotation="varimax",scores = "regression"))) %>% 
  mutate(model.fa2 = map(data, function(df) factanal(df,2,rotation="varimax",scores = "regression"))) %>% 
  mutate(model.fa3 = map(data, function(df) factanal(df,3,rotation="varimax",scores = "regression"))) %>%
  mutate(model.mfa = map(data, function (df) MFA(df,group = c(1,1,1,1,1,1), type=c(rep("s",1),rep("s",1),rep("s",1),rep("s",1),rep("s",1),rep("s",1)),name.group = c("Body Size","Longevity","Clutch size","Age at breeding","Brood freq","Hatchling mass"),
                                                 ncp = 5,graph = F))) %>% 
  group_by(Class) %>% 
  mutate(model.fa1.r = map(model.fa1, function(model) broom::tidy(model)), 
         model.fa2.r = map(model.fa2, function(model) broom::tidy(model)),
         model.fa3.r = map(model.fa3, function(model) broom::tidy(model))) %>% 
  mutate(model.fa1.r = map(model.fa1.r, function (df) mutate(df, com.var = 1 - uniqueness)),
         model.fa2.r = map(model.fa2.r, function (df) mutate(df, com.var = 1 - uniqueness)),
         model.fa3.r = map(model.fa3.r, function (df) mutate(df, com.var = 1 - uniqueness))) %>% 
  mutate(mfa.coord = map(model.mfa,function(mfa) mfa$quanti.var$coord[,1:3]))

# check the data
tetrapod_nested

## # A tibble: 5 x 10
## # Groups:   Class [5]
##   Class data  model.fa1 model.fa2 model.fa3 model.mfa model.fa1.r
##   <chr> <lis> <list>    <list>    <list>    <list>    <list>     
## 1 Amph… <tib… <factana… <factana… <factana… <MFA>     <tibble [6…
## 2 Aves  <tib… <factana… <factana… <factana… <MFA>     <tibble [6…
## 3 Mamm… <tib… <factana… <factana… <factana… <MFA>     <tibble [6…
## 4 Rept… <tib… <factana… <factana… <factana… <MFA>     <tibble [6…
## 5 Tetr… <tib… <factana… <factana… <factana… <MFA>     <tibble [6…
## # … with 3 more variables: model.fa2.r <list>, model.fa3.r <list>,
## #   mfa.coord <list>

Mammals

Multiple Factor Analysis (MFA)

Create the subset dataset

mammals<- tetrapod_nested %>% 
  filter(Class == "Mammalia")

Check the percentage for each axis in the MFA

map(mammals$model.mfa,~fviz_screeplot(.))

## [[1]]

We see that the first dimention explain most of the variation so we will plot the first and the second. Now we will explore the results.

First lets see how they disperse in space

map(mammals$model.mfa,~fviz_mfa_var(., "quanti.var", palette = "jco", 
             col.var.sup = "violet", repel = TRUE,
             geom = c("point", "text"), legend = "none",title = "Mammals"))

## [[1]]

Explore the contribution of each trait to the axes

#the contribution of the first axis
pm1<- map(mammals$model.mfa,~fviz_contrib(., "group", axes = 1,title= "Contribution of traits to first axis-mammals"))
pm2<- map(mammals$model.mfa,~fviz_contrib(., "group", axes = 2,title= "Contribution of traits to second axis-mammals"))
gm1<- plot_grid(pm1[[1]],pm2[[1]],labels = c("A","B"))
gm1

Plot each point and color it based on its quality of representation

map(mammals$model.mfa,~fviz_mfa_ind(., col.ind = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE,label = "none"))

## [[1]]

Factor Analysis with factanal function

Exploratory power

We can see that in all the factors it’s quite strong exploratory power. We can use the parallel analysis to see how many factors we should use. You see that by looking at where the blue line (the actual data) breaks and where the difference between the blue line and the red line (simulated data) is the smallest. Based on this three might be more sutible but it has 0 degrees of freedom so we will take Two Factors.

parallel <- fa.parallel(mammals$data[[1]], fm = 'ml', fa = 'fa')

## Parallel analysis suggests that the number of factors =  3  and the number of components =  NA

The results for Three factors

The common variance (column com.var) shows how much of the variance is shared between a specific variable and the rest of the variables. The larger the number the more informative the variable.

knitr::kable(print(mammals$model.fa2.r))

## [[1]]
## # A tibble: 6 x 5
##   variable           uniqueness    fl1    fl2 com.var
##   <chr>                   <dbl>  <dbl>  <dbl>   <dbl>
## 1 Log_Female_Mass         0.202  0.471  0.759   0.798
## 2 log_longevity           0.226  0.746  0.465   0.774
## 3 log_clutch              0.559 -0.520 -0.413   0.441
## 4 log_breading_age        0.106  0.872  0.367   0.894
## 5 log_brood               0.307 -0.778 -0.295   0.693
## 6 Log_Hatchling_Mass      0.005  0.349  0.934   0.995

variable	uniqueness	fl1	fl2	com.var
Log_Female_Mass	0.2024090	0.4709061	0.7588400	0.7975910
log_longevity	0.2263958	0.7463529	0.4653622	0.7736042
log_clutch	0.5592237	-0.5195702	-0.4133064	0.4407763
log_breading_age	0.1055722	0.8717895	0.3666210	0.8944278
log_brood	0.3071465	-0.7781869	-0.2954299	0.6928535
Log_Hatchling_Mass	0.0050000	0.3493945	0.9343044	0.9950000

Factor analysis plot

ggplot(mammals$model.fa2.r[[1]],aes(fl1,fl2))+
  theme_geometry(mammals$model.fa2.r[[1]]$fl1,mammals$model.fa2.r[[1]]$fl2)+
  geom_point()+
  geom_text(aes(label=variable),hjust=0.5, vjust=-1)

Birds

Multiple Factor Analysis (MFA)

Create the subset dataset

birds<- tetrapod_nested %>% 
  filter(Class == "Aves")

Check the percentage for each axis in the MFA

map(birds$model.mfa,~fviz_screeplot(.))

## [[1]]

We see that the first dimention explain most of the variation so we will plot the first and the second. Now we will explore the results.

First lets see how they disperse in space

map(birds$model.mfa,~fviz_mfa_var(., "quanti.var", palette = "jco", 
             col.var.sup = "violet", repel = TRUE,
             geom = c("point", "text"), legend = "none",title = "Birds"))

## [[1]]

Explore the contribution of each trait to the axes

#the contribution of the first axis
pm1<- map(birds$model.mfa,~fviz_contrib(., "group", axes = 1,title= "Contribution of traits to first axis-mammals"))
pm2<- map(birds$model.mfa,~fviz_contrib(., "group", axes = 2,title= "Contribution of traits to second axis-mammals"))
gm1<- plot_grid(pm1[[1]],pm2[[1]],labels = c("A","B"))
gm1

Plot each point and color it based on its quality of representation

map(birds$model.mfa,~fviz_mfa_ind(., col.ind = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE,label = "none"))

## [[1]]

Factor Analysis with factanal function

Exploratory power

We can see that in all the factors it’s quite strong exploratory power. We can use the parallel analysis to see how many factors we should use. In our case it’s Two Factors

parallel <- fa.parallel(birds$data[[1]], fm = 'ml', fa = 'fa')

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA

The results for Two factors

The common variance (column com.var) shows how much of the variance is shared between a specific variable and the rest of the variables. The larger the number the more informative the variable.

knitr::kable(print(birds$model.fa2.r))

## [[1]]
## # A tibble: 6 x 5
##   variable           uniqueness    fl1    fl2 com.var
##   <chr>                   <dbl>  <dbl>  <dbl>   <dbl>
## 1 Log_Female_Mass       0.00812  0.986  0.141   0.992
## 2 log_longevity         0.514    0.575  0.395   0.486
## 3 log_clutch            0.420   -0.125 -0.751   0.580
## 4 log_breading_age      0.160    0.542  0.739   0.840
## 5 log_brood             0.756   -0.420 -0.260   0.244
## 6 Log_Hatchling_Mass    0.0731   0.916  0.296   0.927

variable	uniqueness	fl1	fl2	com.var
Log_Female_Mass	0.0081211	0.9858722	0.1411915	0.9918789
log_longevity	0.5138691	0.5747281	0.3947403	0.4861309
log_clutch	0.4198854	-0.1252311	-0.7512836	0.5801146
log_breading_age	0.1601473	0.5417116	0.7391895	0.8398527
log_brood	0.7561382	-0.4199588	-0.2598803	0.2438618
Log_Hatchling_Mass	0.0731074	0.9160586	0.2961911	0.9268926

Factor analysis plot

ggplot(birds$model.fa2.r[[1]],aes(fl1,fl2))+
  theme_geometry(birds$model.fa2.r[[1]]$fl1,birds$model.fa2.r[[1]]$fl2)+
  geom_point()+
  geom_text(aes(label=variable),hjust=0.5, vjust=-1)

Reptiles

Multiple Factor Analysis (MFA)

Create the subset dataset

reptiles<- tetrapod_nested %>% 
  filter(Class == "Reptilia")

Check the percentage for each axis in the MFA

map(reptiles$model.mfa,~fviz_screeplot(.))

## [[1]]

We see that the first dimention explain most of the variation so we will plot the first and the second. Now we will explore the results.

First lets see how they disperse in space

map(reptiles$model.mfa,~fviz_mfa_var(., "quanti.var", palette = "jco", 
             col.var.sup = "violet", repel = TRUE,
             geom = c("point", "text"), legend = "none",title = "Reptiles"))

## [[1]]

Explore the contribution of each trait to the axes

#the contribution of the first axis
pm1<- map(reptiles$model.mfa,~fviz_contrib(., "group", axes = 1,title= "Contribution of traits to first axis-mammals"))
pm2<- map(reptiles$model.mfa,~fviz_contrib(., "group", axes = 2,title= "Contribution of traits to second axis-mammals"))
gm1<- plot_grid(pm1[[1]],pm2[[1]],labels = c("A","B"))
gm1

Plot each point and color it based on its quality of representation

map(reptiles$model.mfa,~fviz_mfa_ind(., col.ind = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE,label = "none"))

## [[1]]

Factor Analysis with factanal function

Exploratory power

We can see that in all the factors it’s quite strong exploratory power. We can use the parallel analysis to see how many factors we should use. In our case it’s Two Factors

parallel <- fa.parallel(reptiles$data[[1]], fm = 'ml', fa = 'fa')

## Parallel analysis suggests that the number of factors =  4  and the number of components =  NA

The results for Two factors

The common variance (column com.var) shows how much of the variance is shared between a specific variable and the rest of the variables. The larger the number the more informative the variable.

knitr::kable(print(reptiles$model.fa2.r))

## [[1]]
## # A tibble: 6 x 5
##   variable           uniqueness    fl1    fl2 com.var
##   <chr>                   <dbl>  <dbl>  <dbl>   <dbl>
## 1 Log_Female_Mass         0.005  0.531  0.844  0.995 
## 2 log_longevity           0.108  0.908  0.259  0.892 
## 3 log_clutch              0.532  0.187  0.658  0.468 
## 4 log_breading_age        0.274  0.762  0.380  0.726 
## 5 log_brood               0.961 -0.156 -0.122  0.0392
## 6 Log_Hatchling_Mass      0.172  0.628  0.658  0.828

variable	uniqueness	fl1	fl2	com.var
Log_Female_Mass	0.0050000	0.5311291	0.8443390	0.9950000
log_longevity	0.1082916	0.9080053	0.2592963	0.8917084
log_clutch	0.5323162	0.1871770	0.6577486	0.4676838
log_breading_age	0.2744691	0.7623471	0.3799387	0.7255309
log_brood	0.9607840	-0.1558700	-0.1219647	0.0392160
Log_Hatchling_Mass	0.1722643	0.6283427	0.6579677	0.8277357

Factor analysis plot

ggplot(reptiles$model.fa2.r[[1]],aes(fl1,fl2))+
  theme_geometry(reptiles$model.fa2.r[[1]]$fl1,reptiles$model.fa2.r[[1]]$fl2)+
  geom_point()+
  geom_text(aes(label=variable),hjust=0.5, vjust=-1)

Amphibians

Multiple Factor Analysis (MFA)

Create the subset dataset

amph<- tetrapod_nested %>% 
  filter(Class == "Amphibia")

Check the percentage for each axis in the MFA

map(amph$model.mfa,~fviz_screeplot(.))

## [[1]]

We see that the first dimention explain most of the variation so we will plot the first and the second. Now we will explore the results.

First lets see how they disperse in space

map(amph$model.mfa,~fviz_mfa_var(., "quanti.var", palette = "jco", 
             col.var.sup = "violet", repel = TRUE,
             geom = c("point", "text"), legend = "none",title = "Amphibians"))

## [[1]]

Explore the contribution of each trait to the axes

#the contribution of the first axis
pm1<- map(amph$model.mfa,~fviz_contrib(., "group", axes = 1,title= "Contribution of traits to first axis-mammals"))
pm2<- map(amph$model.mfa,~fviz_contrib(., "group", axes = 2,title= "Contribution of traits to second axis-mammals"))
gm1<- plot_grid(pm1[[1]],pm2[[1]],labels = c("A","B"))
gm1

Plot each point and color it based on its quality of representation

map(amph$model.mfa,~fviz_mfa_ind(., col.ind = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE,label = "none"))

## [[1]]

Factor Analysis with factanal function

Exploratory power

We can see that in all the factors it’s quite strong exploratory power. We can use the parallel analysis to see how many factors we should use. In our case it’s Two Factors

parallel <- fa.parallel(amph$data[[1]], fm = 'ml', fa = 'fa')

## Parallel analysis suggests that the number of factors =  2  and the number of components =  NA

The results for Two factors

The common variance (column com.var) shows how much of the variance is shared between a specific variable and the rest of the variables. The larger the number the more informative the variable.

In here you see that some of the variables don’t add much to the model (com.var is low)

knitr::kable(print(amph$model.fa2.r))

## [[1]]
## # A tibble: 6 x 5
##   variable           uniqueness     fl1     fl2 com.var
##   <chr>                   <dbl>   <dbl>   <dbl>   <dbl>
## 1 Log_Female_Mass         0.712  0.509   0.170    0.288
## 2 log_longevity           0.214  0.884   0.0708   0.786
## 3 log_clutch              0.005 -0.125   0.990    0.995
## 4 log_breading_age        0.605  0.615  -0.128    0.395
## 5 log_brood               0.883 -0.342  -0.0145   0.117
## 6 Log_Hatchling_Mass      0.871 -0.0843 -0.350    0.129

variable	uniqueness	fl1	fl2	com.var
Log_Female_Mass	0.7116636	0.5094013	0.1698506	0.2883364
log_longevity	0.2139989	0.8837348	0.0707921	0.7860011
log_clutch	0.0050000	-0.1248152	0.9896571	0.9950000
log_breading_age	0.6051064	0.6152799	-0.1276403	0.3948936
log_brood	0.8830899	-0.3416131	-0.0145175	0.1169101
Log_Hatchling_Mass	0.8705508	-0.0842664	-0.3497850	0.1294492

Factor analysis plot

ggplot(amph$model.fa2.r[[1]],aes(fl1,fl2))+
  theme_geometry(amph$model.fa2.r[[1]]$fl1,amph$model.fa2.r[[1]]$fl2)+
  geom_point()+
  geom_text(aes(label=variable),hjust=0.5, vjust=-1)

All tetrapods

Multiple Factor Analysis (MFA)

Create the subset dataset

all.tetrapods<- tetrapod_nested %>% 
  filter(Class == "Tetrapods")

Check the percentage for each axis in the MFA

map(all.tetrapods$model.mfa,~fviz_screeplot(.))

## [[1]]

We see that the first dimention explain most of the variation so we will plot the first and the second. Now we will explore the results.

First lets see how they disperse in space

map(all.tetrapods$model.mfa,~fviz_mfa_var(., "quanti.var", palette = "jco", 
             col.var.sup = "violet", repel = TRUE,
             geom = c("point", "text"), legend = "none",title = "All tetrapods"))

## [[1]]

Explore the contribution of each trait to the axes

#the contribution of the first axis
pm1<- map(all.tetrapods$model.mfa,~fviz_contrib(., "group", axes = 1,title= "Contribution of traits to first axis-mammals"))
pm2<- map(all.tetrapods$model.mfa,~fviz_contrib(., "group", axes = 2,title= "Contribution of traits to second axis-mammals"))
gm1<- plot_grid(pm1[[1]],pm2[[1]],labels = c("A","B"))
gm1

Plot each point and color it based on its quality of representation

map(all.tetrapods$model.mfa,~fviz_mfa_ind(., col.ind = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE,label = "none"))

## [[1]]

Factor Analysis with factanal function

Exploratory power

We can see that in all the factors it’s quite strong exploratory power. We can use the parallel analysis to see how many factors we should use. In our case it’s Two Factors

parallel <- fa.parallel(all.tetrapods$data[[1]], fm = 'ml', fa = 'fa')

## Parallel analysis suggests that the number of factors =  3  and the number of components =  NA

The results for Two factors

The common variance (column com.var) shows how much of the variance is shared between a specific variable and the rest of the variables. The larger the number the more informative the variable.

knitr::kable(print(all.tetrapods$model.fa2.r))

## [[1]]
## # A tibble: 6 x 5
##   variable           uniqueness     fl1      fl2 com.var
##   <chr>                   <dbl>   <dbl>    <dbl>   <dbl>
## 1 Log_Female_Mass         0.181  0.520   0.741     0.819
## 2 log_longevity           0.321  0.779   0.269     0.679
## 3 log_clutch              0.777  0.0127 -0.472     0.223
## 4 log_breading_age        0.222  0.882   0.00332   0.778
## 5 log_brood               0.718 -0.459  -0.267     0.282
## 6 Log_Hatchling_Mass      0.005  0.432   0.899     0.995

variable	uniqueness	fl1	fl2	com.var
Log_Female_Mass	0.1810837	0.5199908	0.7406257	0.8189163
log_longevity	0.3211015	0.7789730	0.2685122	0.6788985
log_clutch	0.7772686	0.0127173	-0.4717750	0.2227314
log_breading_age	0.2219011	0.8820929	0.0033205	0.7780989
log_brood	0.7178213	-0.4592167	-0.2670217	0.2821787
Log_Hatchling_Mass	0.0050000	0.4320945	0.8990557	0.9950000

Factor analysis plot

ggplot(all.tetrapods$model.fa2.r[[1]],aes(fl1,fl2))+
  theme_geometry(all.tetrapods$model.fa2.r[[1]]$fl1,all.tetrapods$model.fa2.r[[1]]$fl2)+
  geom_point()+
  geom_text(aes(label=variable),hjust=0.5, vjust=-1)

---
title: "Factor Analysis with female body mass"
author: "Maria Novosolov"
date: "`r Sys.Date()`"
output: 
  html_document:
    toc: true
    toc_float: true
    toc_depth: 4
    theme: united
    highlight: tango
    code_folding: show
    code_download: true
    font: FiraCode
---

Load the libraries
```{r}
knitr::opts_knit$set(root.dir =  rprojroot::find_rstudio_root_file())
knitr::opts_chunk$set(echo = TRUE)
pacman::p_load(tidyverse,vegan,GPArotation,psych,MASS,factoextra,cluster,fpc,FactoMineR,cowplot,broom,modelr,psy)

```

### Create the curated dataset

Log transform what is needed and select the needed columns
```{r}
source("scripts/theme_geometry.R")
tetrapod_data<- readr::read_csv("data/Tetrapod life history database for maria 31.1.20.csv") %>% 
  drop_na() %>% 
  mutate(log_longevity = log10(Max_Longevity),
         log_clutch = log10(Clutch_Litter_size),
         log_breading_age = log10(Mean_age_at_breeding),
         log_brood = log10(Maximum_Broods_per_year))

tetrapod_data<- tetrapod_data %>% 
  dplyr::select(Class, Log_Female_Mass, log_longevity,log_clutch,log_breading_age,log_brood,Log_Hatchling_Mass)

head(tetrapod_data)

```

Running the FA model and extracting the factors for 1,2, and 3 factors. And running the MFA model
Storing everything in a nested dataset
```{r}
#create a nested dataset with all the tetrapods
all_tetra_nest<- tetrapod_data %>% 
  dplyr::select(-Class) %>% 
  nest() %>%
  add_column(Class = "Tetrapods",.before = 1)

#create a nested dataset by class, add the whole tetrapods and map the models into them
tetrapod_nested<- tetrapod_data %>%
  nest(-Class) %>%
  bind_rows(all_tetra_nest) %>% 
  mutate(model.fa1 = map(data, function(df) factanal(df,1,rotation="varimax",scores = "regression"))) %>% 
  mutate(model.fa2 = map(data, function(df) factanal(df,2,rotation="varimax",scores = "regression"))) %>% 
  mutate(model.fa3 = map(data, function(df) factanal(df,3,rotation="varimax",scores = "regression"))) %>%
  mutate(model.mfa = map(data, function (df) MFA(df,group = c(1,1,1,1,1,1), type=c(rep("s",1),rep("s",1),rep("s",1),rep("s",1),rep("s",1),rep("s",1)),name.group = c("Body Size","Longevity","Clutch size","Age at breeding","Brood freq","Hatchling mass"),
                                                 ncp = 5,graph = F))) %>% 
  group_by(Class) %>% 
  mutate(model.fa1.r = map(model.fa1, function(model) broom::tidy(model)), 
         model.fa2.r = map(model.fa2, function(model) broom::tidy(model)),
         model.fa3.r = map(model.fa3, function(model) broom::tidy(model))) %>% 
  mutate(model.fa1.r = map(model.fa1.r, function (df) mutate(df, com.var = 1 - uniqueness)),
         model.fa2.r = map(model.fa2.r, function (df) mutate(df, com.var = 1 - uniqueness)),
         model.fa3.r = map(model.fa3.r, function (df) mutate(df, com.var = 1 - uniqueness))) %>% 
  mutate(mfa.coord = map(model.mfa,function(mfa) mfa$quanti.var$coord[,1:3]))

# check the data
tetrapod_nested
```

## Mammals {.tabset}

### Multiple Factor Analysis (MFA)

Create the subset dataset

```{r}
mammals<- tetrapod_nested %>% 
  filter(Class == "Mammalia")
```

Check the percentage for each axis in the MFA 
```{r}
map(mammals$model.mfa,~fviz_screeplot(.))
```

We see that the first dimention explain most of the variation so we will plot the first and the second.
Now we will explore the results. 

First lets see how they disperse in space
```{r}
map(mammals$model.mfa,~fviz_mfa_var(., "quanti.var", palette = "jco", 
             col.var.sup = "violet", repel = TRUE,
             geom = c("point", "text"), legend = "none",title = "Mammals"))
```

Explore the contribution of each trait to the axes
```{r}
#the contribution of the first axis
pm1<- map(mammals$model.mfa,~fviz_contrib(., "group", axes = 1,title= "Contribution of traits to first axis-mammals"))
pm2<- map(mammals$model.mfa,~fviz_contrib(., "group", axes = 2,title= "Contribution of traits to second axis-mammals"))
gm1<- plot_grid(pm1[[1]],pm2[[1]],labels = c("A","B"))
gm1

```

Plot each point and color it based on its quality of representation 
```{r}
map(mammals$model.mfa,~fviz_mfa_ind(., col.ind = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE,label = "none"))
```


### Factor Analysis with factanal function

#### Exploratory power

We can see that in all the factors it's quite strong exploratory power.
We can use the parallel analysis to see how many factors we should use. You see that by looking at where the blue line (the actual data) breaks and where the difference between the blue line and the red line (simulated data) is the smallest. Based on this three might be more sutible but it has 0 degrees of freedom so we will take **Two Factors**. 

```{r}
parallel <- fa.parallel(mammals$data[[1]], fm = 'ml', fa = 'fa')
```


**The results for Three factors**

The common variance (column com.var) shows how much of the variance is shared between a specific variable and the rest of the variables. The larger the number the more informative the variable.

```{r}
knitr::kable(print(mammals$model.fa2.r))
```

#### Factor analysis plot

```{r}
ggplot(mammals$model.fa2.r[[1]],aes(fl1,fl2))+
  theme_geometry(mammals$model.fa2.r[[1]]$fl1,mammals$model.fa2.r[[1]]$fl2)+
  geom_point()+
  geom_text(aes(label=variable),hjust=0.5, vjust=-1)
```

## Birds {.tabset}

### Multiple Factor Analysis (MFA)

Create the subset dataset

```{r}
birds<- tetrapod_nested %>% 
  filter(Class == "Aves")
```

Check the percentage for each axis in the MFA 
```{r}
map(birds$model.mfa,~fviz_screeplot(.))
```

We see that the first dimention explain most of the variation so we will plot the first and the second.
Now we will explore the results. 

First lets see how they disperse in space
```{r}
map(birds$model.mfa,~fviz_mfa_var(., "quanti.var", palette = "jco", 
             col.var.sup = "violet", repel = TRUE,
             geom = c("point", "text"), legend = "none",title = "Birds"))
```

Explore the contribution of each trait to the axes
```{r}
#the contribution of the first axis
pm1<- map(birds$model.mfa,~fviz_contrib(., "group", axes = 1,title= "Contribution of traits to first axis-mammals"))
pm2<- map(birds$model.mfa,~fviz_contrib(., "group", axes = 2,title= "Contribution of traits to second axis-mammals"))
gm1<- plot_grid(pm1[[1]],pm2[[1]],labels = c("A","B"))
gm1

```

Plot each point and color it based on its quality of representation 
```{r}
map(birds$model.mfa,~fviz_mfa_ind(., col.ind = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE,label = "none"))
```


### Factor Analysis with factanal function

#### Exploratory power

We can see that in all the factors it's quite strong exploratory power.
We can use the parallel analysis to see how many factors we should use. In our case it's **Two Factors**

```{r}
parallel <- fa.parallel(birds$data[[1]], fm = 'ml', fa = 'fa')
```


**The results for Two factors**

The common variance (column com.var) shows how much of the variance is shared between a specific variable and the rest of the variables. The larger the number the more informative the variable.

```{r}
knitr::kable(print(birds$model.fa2.r))
```

#### Factor analysis plot

```{r}
ggplot(birds$model.fa2.r[[1]],aes(fl1,fl2))+
  theme_geometry(birds$model.fa2.r[[1]]$fl1,birds$model.fa2.r[[1]]$fl2)+
  geom_point()+
  geom_text(aes(label=variable),hjust=0.5, vjust=-1)
```


## Reptiles {.tabset}

### Multiple Factor Analysis (MFA)

Create the subset dataset

```{r}
reptiles<- tetrapod_nested %>% 
  filter(Class == "Reptilia")
```

Check the percentage for each axis in the MFA 
```{r}
map(reptiles$model.mfa,~fviz_screeplot(.))
```

We see that the first dimention explain most of the variation so we will plot the first and the second.
Now we will explore the results. 

First lets see how they disperse in space
```{r}
map(reptiles$model.mfa,~fviz_mfa_var(., "quanti.var", palette = "jco", 
             col.var.sup = "violet", repel = TRUE,
             geom = c("point", "text"), legend = "none",title = "Reptiles"))
```

Explore the contribution of each trait to the axes
```{r}
#the contribution of the first axis
pm1<- map(reptiles$model.mfa,~fviz_contrib(., "group", axes = 1,title= "Contribution of traits to first axis-mammals"))
pm2<- map(reptiles$model.mfa,~fviz_contrib(., "group", axes = 2,title= "Contribution of traits to second axis-mammals"))
gm1<- plot_grid(pm1[[1]],pm2[[1]],labels = c("A","B"))
gm1

```

Plot each point and color it based on its quality of representation 
```{r}
map(reptiles$model.mfa,~fviz_mfa_ind(., col.ind = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE,label = "none"))
```


### Factor Analysis with factanal function

#### Exploratory power

We can see that in all the factors it's quite strong exploratory power.
We can use the parallel analysis to see how many factors we should use. In our case it's **Two Factors**

```{r}
parallel <- fa.parallel(reptiles$data[[1]], fm = 'ml', fa = 'fa')
```


**The results for Two factors**

The common variance (column com.var) shows how much of the variance is shared between a specific variable and the rest of the variables. The larger the number the more informative the variable.

```{r}
knitr::kable(print(reptiles$model.fa2.r))
```

#### Factor analysis plot

```{r}
ggplot(reptiles$model.fa2.r[[1]],aes(fl1,fl2))+
  theme_geometry(reptiles$model.fa2.r[[1]]$fl1,reptiles$model.fa2.r[[1]]$fl2)+
  geom_point()+
  geom_text(aes(label=variable),hjust=0.5, vjust=-1)
```

## Amphibians {.tabset}

### Multiple Factor Analysis (MFA)

Create the subset dataset

```{r}
amph<- tetrapod_nested %>% 
  filter(Class == "Amphibia")
```

Check the percentage for each axis in the MFA 
```{r}
map(amph$model.mfa,~fviz_screeplot(.))
```

We see that the first dimention explain most of the variation so we will plot the first and the second.
Now we will explore the results. 

First lets see how they disperse in space
```{r}
map(amph$model.mfa,~fviz_mfa_var(., "quanti.var", palette = "jco", 
             col.var.sup = "violet", repel = TRUE,
             geom = c("point", "text"), legend = "none",title = "Amphibians"))
```

Explore the contribution of each trait to the axes
```{r}
#the contribution of the first axis
pm1<- map(amph$model.mfa,~fviz_contrib(., "group", axes = 1,title= "Contribution of traits to first axis-mammals"))
pm2<- map(amph$model.mfa,~fviz_contrib(., "group", axes = 2,title= "Contribution of traits to second axis-mammals"))
gm1<- plot_grid(pm1[[1]],pm2[[1]],labels = c("A","B"))
gm1

```

Plot each point and color it based on its quality of representation 
```{r}
map(amph$model.mfa,~fviz_mfa_ind(., col.ind = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE,label = "none"))
```


### Factor Analysis with factanal function

#### Exploratory power

We can see that in all the factors it's quite strong exploratory power.
We can use the parallel analysis to see how many factors we should use. In our case it's **Two Factors**

```{r}
parallel <- fa.parallel(amph$data[[1]], fm = 'ml', fa = 'fa')
```


**The results for Two factors**

The common variance (column com.var) shows how much of the variance is shared between a specific variable and the rest of the variables. The larger the number the more informative the variable.

In here you see that some of the variables don't add much to the model (com.var is low)

```{r}
knitr::kable(print(amph$model.fa2.r))
```

#### Factor analysis plot

```{r}
ggplot(amph$model.fa2.r[[1]],aes(fl1,fl2))+
  theme_geometry(amph$model.fa2.r[[1]]$fl1,amph$model.fa2.r[[1]]$fl2)+
  geom_point()+
  geom_text(aes(label=variable),hjust=0.5, vjust=-1)
```


## All tetrapods {.tabset}

### Multiple Factor Analysis (MFA)

Create the subset dataset

```{r}
all.tetrapods<- tetrapod_nested %>% 
  filter(Class == "Tetrapods")
```

Check the percentage for each axis in the MFA 
```{r}
map(all.tetrapods$model.mfa,~fviz_screeplot(.))
```

We see that the first dimention explain most of the variation so we will plot the first and the second.
Now we will explore the results. 

First lets see how they disperse in space
```{r}
map(all.tetrapods$model.mfa,~fviz_mfa_var(., "quanti.var", palette = "jco", 
             col.var.sup = "violet", repel = TRUE,
             geom = c("point", "text"), legend = "none",title = "All tetrapods"))
```

Explore the contribution of each trait to the axes
```{r}
#the contribution of the first axis
pm1<- map(all.tetrapods$model.mfa,~fviz_contrib(., "group", axes = 1,title= "Contribution of traits to first axis-mammals"))
pm2<- map(all.tetrapods$model.mfa,~fviz_contrib(., "group", axes = 2,title= "Contribution of traits to second axis-mammals"))
gm1<- plot_grid(pm1[[1]],pm2[[1]],labels = c("A","B"))
gm1

```

Plot each point and color it based on its quality of representation 
```{r}
map(all.tetrapods$model.mfa,~fviz_mfa_ind(., col.ind = "cos2",
             gradient.cols = c("#00AFBB", "#E7B800", "#FC4E07"),
             repel = TRUE,label = "none"))
```


### Factor Analysis with factanal function

#### Exploratory power

We can see that in all the factors it's quite strong exploratory power.
We can use the parallel analysis to see how many factors we should use. In our case it's **Two Factors**

```{r}
parallel <- fa.parallel(all.tetrapods$data[[1]], fm = 'ml', fa = 'fa')
```


**The results for Two factors**

The common variance (column com.var) shows how much of the variance is shared between a specific variable and the rest of the variables. The larger the number the more informative the variable.

```{r}
knitr::kable(print(all.tetrapods$model.fa2.r))
```

#### Factor analysis plot

```{r}
ggplot(all.tetrapods$model.fa2.r[[1]],aes(fl1,fl2))+
  theme_geometry(all.tetrapods$model.fa2.r[[1]]$fl1,all.tetrapods$model.fa2.r[[1]]$fl2)+
  geom_point()+
  geom_text(aes(label=variable),hjust=0.5, vjust=-1)
```



Factor Analysis with female body mass

Maria Novosolov

2020-02-07

Create the curated dataset

Mammals

Multiple Factor Analysis (MFA)

Factor Analysis with factanal function

Exploratory power

Factor analysis plot

Birds

Multiple Factor Analysis (MFA)

Factor Analysis with factanal function

Exploratory power

Factor analysis plot

Reptiles

Multiple Factor Analysis (MFA)

Factor Analysis with factanal function

Exploratory power

Factor analysis plot

Amphibians

Multiple Factor Analysis (MFA)

Factor Analysis with factanal function

Exploratory power

Factor analysis plot

All tetrapods

Multiple Factor Analysis (MFA)

Factor Analysis with factanal function

Exploratory power

Factor analysis plot